Use a Brillo pad and w/up liquid + elbow grease.
If you use a Brillo pad, it will scratch the finish.
I'm sorry to recommend this, but it does work. Ammonia will dissolve/loosen the burned-on grease. Soak toweling with it. Cover the grease. Leave it to soak as long as necessary. Scrub it off with a non-scratch pad. You may have to do it more than once.
I hate the smell, but I also hate the burned-on grease.
Don't use Brillo, it will scratch the paint. I use odor free oven cleaner. It doesn't harm the surface. Make sure to use as hot of water with a green/yellow scotchbright sponge. If it's really bad, you can do it a couple times. Finish up with extremely hot watch and dawn. I boil water on another burner and dip the sponge. Make sure to use cleaning gloves like Playtex so you can withstand the hotter water.
Use Dawn soap directly on the wash rag and wipe it off. Also Simple Green is a good degreaser. For the grill grates on top, put them in the dishwasher. (Check your stove manuel, but mine says to put them in the dishwasher! ) I also use dish cloths that have a plastic grid on the back to help scrub those stubborn spots. It does not scratch my stove at all. You can get the double sided dish cloths at Walmart in the home or house wares.